Pearson's correlation measures the linear component of association.
It will be +1 if a plot of one variable against another has all points exactly on an upward-sloping line, and -1 if all points are exactly on a downward-sloping line. If there is little or no linear aspect of association then Pearson's correlation will be near 0.
Spearman's correlation is based on ranks, and may give misleading results if there are more than a few tied values in either variable. If y always increases when x increases, then the value will be +1 whether or not the progression is linear.
It would not be appropriate to suggest one method over the other without knowing more about your data, and your purpose for wanting
to look at the association between two variables.
In the following example, there is an exact linear relationship
between X and Y, and the relationship between X and Z is strong
but not linear. It may be a clearer example if you make
two plots: (a) x vs. y, and (b) x vs. Z.
x: 1 2 3 4 5 6 7 8 9 10
y: 5 7 9 11 13 15 17 19 21 23
z: 1 2 3 5 7 10 20 50 100 300
cor(x,y) # Pearson
## 1
cor(x,z) # Pearson
## 0.7200748
cor(x, z, method="spearman")
## 1
